To find the points where the tangents are horizontal/vertical, we need to find dy/dx. Using the chain rule fore differentiation, we can write
Use product rule for differentiation
Divide both the numerator and the denominator by
The tangents will be horizontal when the numerator is 0
Divide both sides by
In the right-hand side, we will rewrite -1 as
Remember that: the general solution of the equation
Therefore, the tangents are horizontal when
The tangents will be vertical when the denomiantor is 0
Divides both sides by
In the right-hand side, we will rewrite 1 as
Therefore, the tangents are vertical when
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How to write in scientific notation?